Posle sastanka ću probati patike koje su u prodavnici.

Because posle requires the genitive case. The base noun is sastanak meaning meeting, and its genitive singular form is sastanka.

So:

• sastanak = meeting
• posle sastanka = after the meeting / after a meeting

It means after the meeting. Literally:

• posle = after
• sastanka = of the meeting

Serbian often uses a preposition plus a case ending where English just uses a fixed phrase.

This is a normal way to form the future tense in Serbian:

• ću = I will
• probati = try

So ću probati = I will try.

In Serbian, ću is a clitic, which means it usually goes in the second position of the sentence or clause. Since the sentence begins with Posle sastanka, the ću comes right after that opening phrase:

• Posle sastanka ću probati...

Yes. Probaću is another correct future form, made by combining the verb with ću.

So these are both possible:

• Posle sastanka ću probati patike...
• Posle sastanka probaću patike...

The version with separate ću is very common, especially when another phrase comes first.

It is in the accusative plural because it is the direct object of probati:

• probati šta? → patike

For this noun, the accusative plural looks the same as the nominative plural, so the form stays patike.

Patike is plural and usually refers to sneakers/trainers/a pair of sneakers in normal usage.

• patika = one sneaker
• patike = sneakers / a pair of sneakers

So in this sentence, the speaker is going to try on the sneakers.

Koje is a relative pronoun meaning which / that. It refers back to patike.

It has to match patike in gender and number:

• patike = feminine plural
• therefore koje = feminine plural form

So:

• patike koje su u prodavnici = the sneakers that are in the store

Because koje is the subject of the relative clause:

• koje su u prodavnici = which are in the store

Here, the sneakers are the ones that are in the store, so the pronoun needs the nominative plural form, which is koje.

It identifies which sneakers the speaker means.

Without that part:

• Posle sastanka ću probati patike. = After the meeting I will try on sneakers.

With the relative clause:

• Posle sastanka ću probati patike koje su u prodavnici. = After the meeting I will try on the sneakers that are in the store.

So it narrows down the meaning.

Because u can take two different cases depending on meaning:

• u + locative = location, in
• u + accusative = motion toward, into

Here the meaning is location:

• u prodavnici = in the store

If it were motion, it would be:

• u prodavnicu = into the store

Here probati means to try on.

That verb can have several meanings depending on context, such as:

• try
• test
• taste
• try on

Because the object is patike, the natural meaning is try on sneakers/shoes.

Probati is perfective. That means it presents the action as a single complete event.

In this sentence, that fits well because the speaker means one planned action in the future:

• I’ll try them on

The imperfective partner would be something like probavati, which would suggest repeated trying or an ongoing/habitual action, and would sound less natural here.

Serbian has no articles, so there is no direct equivalent of the or a/an.

Definiteness is understood from context. In this sentence:

• sastanka can mean the meeting or a meeting, depending on context
• patike koje su u prodavnici sounds fairly specific because the relative clause identifies them

So Serbian leaves that to context instead of using articles.

Yes, Serbian word order is fairly flexible. But the clitic ću still has to follow normal clitic placement rules.

The original sentence is natural and emphasizes when the action happens:

• Posle sastanka ću probati patike koje su u prodavnici.

Other versions are possible, for example:

• Probaću patike koje su u prodavnici posle sastanka.

That still means basically the same thing, but the emphasis can shift slightly.

Ću is pronounced roughly like tyoo, but with a softer t sound than in English.

A rough guide:

• ć = a soft sound somewhat like t+y together
• ću ≈ tyoo

It is different from the harder č sound. For English speakers, that contrast can take some practice.